Undergraduate Program in Secondary Mathematics Education

Functions, limits, continuity, differentiation and applications, integration, fundamental theorem of calculus, techniques and applications of integration, improper integrals and series, Taylor polynomials, power series, basic transcendental functions.

Propositional logic and first-order monadic quantifier calculus.

Counting, the pigeonhole principle, permutations, combinations, binomial coefficients, generalized permutations and combinations, discrete probability, linear recurrence relations, generating functions, inclusion-exclusion, relations, closure of relations, equivalence relations, construction of integers and rationals, partial orderings, graphs.

Understanding the human potential, effectiveness and motivation. Human development and diversity. Problem solving, memory and creativity. Instruction and assessment in learning. Contemporary issues in educational psychology.

Sequences and functions, compact sets, continuity, uniform continuity, limits of functions, discontinuities, differentiation, derivatives for functions of several variables, differentiation of composite functions, Taylor's Theorem, definite integrals, substitution in multiple integrals, improper integrals.

Groups, subgroups, cyclic groups, generating sets, permutations, orbits, cycles, alternating groups, cosets, Lagrange's Theorem, direct products, finite abelian groups, homomorphism, normal subgroups, factor groups, simple groups, group actions, isomorphism theorems, Sylow's theorems.

Learning theories, and approaches to curriculum development in mathematics and science; overview of history of mathematics and science education; concepts, principles, methods and techniques of instructional planning in mathematics and science education.

Introduction into the field of guidance and counseling; its conceptualization, historical background, nature, professional roles, direct and indirect functions. A brief review of career counseling, counseling with special groups, basic assessment techniques, and development of these services in Turkiye.

Data processing in educational contexts; analyzing and reporting descriptive statistics; concepts of normal distributions, standard scores and hypothesis testing; biserial and rank order correlations, multiple regression, t-test, ANOVA, applications by using statistical software.

Nature of mathematics, overview of theories in learning mathematics; examining the development of students’ understanding of fundamental concepts of school mathematics; teaching techniques, methods and strategies for mathematics; analyzing, designing and planning instruction.

The concepts and principles of educational technology as an integrated part of teaching and learning process. Basic information technology skills. Selection, development, implementation and evaluation of media with regard to learning theories. Employment of laboratories; audio-visual means, slides, graphs, films and printed materials; computer software including simulations, tutorials, drills, interactive learning environments, microworlds, intelligent systems and multimedia.

Methods of measurement and assessment in mathematics and science education; reliability, validity and practicality in assessment tools; developing tests measuring higher order thinking skills; grading student performance; item analysis; analysis and discussions of national and international assessments.

Survey of research methods related to mathematics and science education; planning a small scale research study focused on these areas.

Critical observation of educational contexts and processes: school organization, school administration, teaching, daily routines, school-family cooperation and school resources; ethical issues in the teaching profession; supervised student teaching.